def RunAcoustic(q):
Nxy = 100
tf = 0.1 # Final time
direction = 0
u0_expr = Expression(\
'100*pow(x[i]-.25,2)*pow(x[i]-0.75,2)*(x[i]<=0.75)*(x[i]>=0.25)', i=direction)
class LeftRight(SubDomain):
def inside(self, x, on_boundary):
return (x[direction] < 1e-16 or x[direction] > 1.0 - 1e-16) \
and on_boundary
h = 1. / Nxy
mesh = UnitSquareMesh(Nxy, Nxy, "crossed")
V = FunctionSpace(mesh, 'Lagrange', q)
Vl = FunctionSpace(mesh, 'Lagrange', 1)
Dt = h / (q * 10.)
Wave = AcousticWave({'V': V, 'Vl': Vl, 'Vr': Vl})
Wave.verbose = True
Wave.lump = True
Wave.set_abc(mesh, LeftRight())
Wave.update({'lambda':1.0, 'rho':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':interpolate(u0_expr, V), 'utinit':Function(V)})
sol, tmp = Wave.solve()
def run_test():
q = 3
Nxy = 100
tf = 0.1
h = 1. / Nxy
mesh = UnitSquareMesh(Nxy, Nxy, "crossed")
V = FunctionSpace(mesh, 'Lagrange', q)
Vl = FunctionSpace(mesh, 'Lagrange', 1)
Dt = h / (q * 10.)
u0_expr = Expression(\
'100*pow(x[i]-.25,2)*pow(x[i]-0.75,2)*(x[i]<=0.75)*(x[i]>=0.25)', i=0)
Wave = AcousticWave({'V': V, 'Vl': Vl, 'Vr': Vl})
Wave.lump = True
Wave.timestepper = 'backward'
Wave.update({'lambda':1.0, 'rho':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':interpolate(u0_expr, V), 'utinit':Function(V)})
K = Wave.K
u = Wave.u0
u.vector()[:] = 1.0
b = Wave.u1
for ii in range(100):
K * u.vector()
(K * u.vector()).array()
b.vector()[:] = (K * u.vector()).array()
b.vector()[:] = 0.0
b.vector().axpy(1.0, K * u.vector())
b.vector()[:] = (K * u.vector()).array() + (K * u.vector()).array()
b.vector()[:] = (K * u.vector() + K * u.vector()).array()
b.vector()[:] = 2.*u.vector().array() + u.vector().array() + \
Dt*u.vector().array()
b.vector()[:] = 0.0
b.vector().axpy(2.0, u.vector())
b.vector().axpy(1.0, u.vector())
b.vector().axpy(Dt, u.vector())
b.assign(u)
b.vector().zero()
#Pt = PointSources(V, [[0.1,y_src], [0.25,y_src], [0.4,y_src],\
#[0.6,y_src], [0.75,y_src], [0.9,y_src]])
Pt = PointSources(V, [[0.1, y_src], [0.4, y_src], [0.6, y_src], [0.9, y_src]])
srcv = dl.Function(V).vector()
# Boundary conditions:
class ABCdom(dl.SubDomain):
def inside(self, x, on_boundary):
return on_boundary and (x[1] < Y)
Wave = AcousticWave({
'V': V,
'Vm': Vl
}, {
'print': False,
'lumpM': True,
'timestepper': 'backward'
})
Wave.set_abc(mesh, ABCdom(), lumpD=False)
at, bt, ct, _, _ = targetmediumparameters(Vl, X)
a0, b0, _, _, _ = initmediumparameters(Vl, X)
Wave.update({'b':bt, 'a':at, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(V), 'utinit':dl.Function(V)})
if PRINT:
print 'nb of src={}, nb of timesteps={}'.format(len(Pt.src_loc), Wave.Nt)
sources, timesteps = partition_work(mpicomm_local, mpicomm_global, \
len(Pt.src_loc), Wave.Nt)
print 'Compute most accurate solution as reference'
qq = 20
N = int(qq / cmin)
h = 1. / N
mesh = dl.UnitSquareMesh(N, N)
Vl = dl.FunctionSpace(mesh, 'Lagrange', 1)
Vex = dl.FunctionSpace(mesh, 'Lagrange', r)
Pt = PointSources(Vex, [[.5, .5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt) * mydelta
Waveex = AcousticWave({'V': Vex, 'Vm': Vl})
Waveex.timestepper = 'backward'
Waveex.lump = True
Waveex.update({'a':1.0, 'b':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(Vex), 'utinit':dl.Function(Vex)})
Waveex.ftime = mysrc
sol, _ = Waveex.solve()
Waveex.exact = dl.Function(Vex)
normex = Waveex.computeabserror()
# plot
myplot.set_varname('u-q' + str(qq))
plotu = dl.Function(Vex)
for index, uu in enumerate(sol):
if index % boolplot == 0:
setfct(plotu, uu[0])
myplot.plot_vtk(plotu, index)
b_target_fn = dl.interpolate(b_target, Vm)
a_target = dl.Expression(\
'1.0 + 0.4*(x[0]<=0.7)*(x[0]>=0.3)*(x[1]<=0.7)*(x[1]>=0.3)')
a_target_fn = dl.interpolate(a_target, Vm)
checkdt(Dt, 1. / Nxy, r, np.sqrt(2.0), False)
# observation operator:
obspts = [[0.0, ii/10.] for ii in range(1,10)] + \
[[1.0, ii/10.] for ii in range(1,10)] + \
[[ii/10., 0.0] for ii in range(1,10)] + \
[[ii/10., 1.0] for ii in range(1,10)]
obsop = TimeObsPtwise({'V': V, 'Points': obspts}, [t0, t1, t2, tf])
# define pde operator:
wavepde = AcousticWave({'V': V, 'Vm': Vm})
wavepde.timestepper = 'backward'
wavepde.lump = True
wavepde.update({'a':a_target_fn, 'b':b_target_fn, \
't0':t0, 'tf':tf, 'Dt':Dt, 'u0init':dl.Function(V), 'utinit':dl.Function(V)})
# parameters
Vm = wavepde.Vm
V = wavepde.V
lenobspts = obsop.PtwiseObs.nbPts
# set up plots:
filename, ext = splitext(sys.argv[0])
if isdir(filename + '/'): rmtree(filename + '/')
myplot = PlotFenics(filename + str(Nxy))
myplot.set_varname('a_target')
class AllFour(SubDomain):
def inside(self, x, on_boundary):
return on_boundary
for r in RR:
V = FunctionSpace(mesh, 'Lagrange', r)
Pt = PointSources(V, [[.5, .5]])
mydelta = Pt[0].array()
def mysrc(tt):
return Ricker(tt) * mydelta
# Computation:
if myrank == 0: print '\n\th = {}, Dt = {}'.format(h, Dt)
Wave = AcousticWave({'V': V, 'Vm': Vl})
#Wave.verbose = True
Wave.timestepper = 'centered'
Wave.lump = True
Wave.set_abc(mesh, AllFour(), True)
Wave.exact = Function(V)
Wave.update({'b':1.0, 'a':1.0, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':Function(V), 'utinit':Function(V)})
Wave.ftime = mysrc
sol, error = Wave.solve()
ERROR.append(error)
if myrank == 0: print 'relative error = {:.5e}'.format(error)
if not mycomm == None: MPI.barrier(mycomm)
# Plots:
try:
V = dl.FunctionSpace(mesh, 'Lagrange', r)
y_src = 1.0 # 0.1->transmission, 1.0->reflection
Pt = PointSources(V, [[0.5 * X, y_src]])
mydelta = Pt[0]
def mysrc(tt):
return mydelta * Ricker(tt)
# Computation:
if mpirank == 0: print '\n\th = {}, Dt = {}'.format(h, Dt)
Wave = AcousticWave({
'V': V,
'Vm': Vl
}, {
'print': (not mpirank),
'lumpM': True,
'timestepper': 'backward'
})
Wave.set_abc(mesh, ABCdom(), lumpD=False)
#Wave.exact = dl.Function(V)
Wave.ftime = mysrc
#
af, bf, _, _, _ = targetmediumparameters(Vl, X, myplot)
#
Wave.update({'b':bf, 'a':af, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':dl.Function(V), 'utinit':dl.Function(V)})
sol, _, _, error = Wave.solve()
if mpirank == 0: print 'relative error = {:.5e}'.format(error)
MPI.barrier(mesh.mpi_comm())
t=tf)
def source(tt):
return Expression('6*(sqrt(pow(x[0]-0.5,2)+pow(x[1]-0.5,2))<=t)', t=tt)
for Nxy in NN:
h = 1. / Nxy
print '\n\th = {}'.format(h)
mesh = UnitSquareMesh(Nxy, Nxy, "crossed")
q = 1 # Polynomial order
V = FunctionSpace(mesh, 'Lagrange', q)
Dt = h / (q * 5. * c)
Wave = AcousticWave({'V': V, 'Vl': V, 'Vr': V})
Wave.timestepper = 'backward'
Wave.lump = True
#Wave.verbose = True
Wave.exact = interpolate(exact_expr, V)
Wave.update({'lambda':lam, 'rho':rho, 't0':0.0, 'tf':tf, 'Dt':Dt,\
'u0init':Function(V), 'utinit':Function(V)})
test = TestFunction(V)
def srcterm(tt):
src_expr = source(tt)
src_vect = assemble(src_expr * test * dx)
return src_vect.array()
Wave.ftime = srcterm
sol, error = Wave.solve()
